To find an equivalent expression to \( \frac{4}{3}(-2 + 1^0) \), we first need to evaluate \( 1^0 \).
According to the rules of exponents, any non-zero number raised to the power of 0 is equal to 1. Therefore:
\[ 1^0 = 1 \]
Now, we can substitute that back into the expression:
\[ -2 + 1^0 = -2 + 1 \]
Now, we can compute:
\[ -2 + 1 = -1 \]
So, we can rewrite the original expression as:
\[ \frac{4}{3}(-2 + 1^0) = \frac{4}{3}(-2 + 1) = \frac{4}{3}(-1) \]
Thus, we can say that an equivalent expression to \( \frac{4}{3}(-2 + 1^0) \) is:
\[ \frac{4}{3}(-2 + (-1)) \]
In the blank, you would place \(-1\).
Thus, the final answer is:
\[ \frac{4}{3}(-2 + \underline{-1}) \]